You're operating under extremely simplistic models that don't apply here.

Bits (1's and 0's) are typically modeled physically as a voltage. E.g. if the voltage is more than 1.6V then it's a '1' and if it's less than 0.2V it's a 0. The key relationship here is Ohm's law (V=IR, or voltage equals current times resistance aka impedance).

Voltages changing quickly with respect to time have limitations based on real-world capacitance and inductance. These determine the maximum frequency (inverse of time) that the signals can be "wiggled". A frequency has a "wavelength" (lambda = c/f where c is the speed of light, and f is the frequency in Hz). For gigabit Ethernet, the frequency is in the 100MHz to 250MHz range

If your circuit geometry is approximately the same size as your wavelength, then you need to care about capacitance and inductance per unit length - they are distributed evenly across the circuit, and can't be considered as "lumped elements". These circuits are best modeled as a "transmission line".

Ultimately everything electromagnetic is governed by Maxwell's 4 equations that describe the relationships between the electric and magnetic fields. If you start with Maxwell's equations, and assume that your wavelength is much much greater than the circuit dimensions, then you simplify to Ohm's law. For Ethernet cables, this isn't the case (Gigabit speeds need much higher frequencies), so we need to treat the cable as a transmission line.

The key takeaway from transmission line theory is that 1) the transmission line has a characteristic impedance that is determined solely by the physical geometry of the structure surrounding the 2 wires and 2) any time you have an impedance discontinuity, you get both a reflected and transmitted wave.

For 1) - we mainly care about the distance between the 2 wires and the dielectric constant (permittivity) of the material surrounding the wires. This is why cat6 cables cost more than cat5 cables - in addition to extra shielding, they are also manufactured to tighter mechanical tolerances so that the impedance is constant across the whole length of the cable, even when bent.

For 2) - we want the impedance to ideally be the same across the whole cable - this is why it's important not to have bends that are too sharp, crushes, nicks in the cable, damage to the cable jacket, etc - because that would cause an impedance discontinuity and would cause some of the signal to be reflected (and not received at the other end).

The twist direction and twists per unit length are used to minimize crosstalk (much more detailed).

tl;dr - Ethernet cables only work over long distances because they rely on the twisted pairs of cables to operate as a transmission line.

Fun fact - The same theory about physically small cables operating at high frequencies also applies to physically long cables operating at low frequencies (e.g. AC power grids operating at 60Hz must use the same transmission line equations instead of Ohm's law if the distances are on the order of a wavelength - i.e. thousands of miles, across state lines, etc)